Stable electromagnetic levitation of spinning conducting cylindrical rotors has been demonstrated theoretically for the first time. General expressions of the quasistationary magnetic vector potential, for a rotating, conducting, cylindrical shell in the proximity of a distribution of parallel straight wires carrying currents, have been obtained by assuming a two-dimensional field. For a practical range of geometric and electric parameters of a thin cylindrical shell rotor, the static stability conditions, losses and torque/speed characteristics are quantitatively derived. Speeds of rotation of up to twenty thousand revolutions per second have been analysed. The results of this study can be applied to the design of electromagnetically levitated and driven rotors.